Question

5. A polyhedron is defined as a three-dimensional object or figure with faces made up of polygons, straight edges and sharp corners or vertices. A polyhedral is named according to the number of faces they have. The learner in a grade six class is confused and says this object is a polyhedron because its net has three faces which are two circles and one rectangle. Provide another object which is not a polyhedron and explain to this leaner the properties of a polyhedron so that the understanding of this concept can be developed and remove the misconceptions and errors this learner has developed. In your explanation, show how you will assist this learner to develop the correct understanding of this concept. (3)​

Answer 1

The object you described with two circles and one rectangle is not a polyhedron because it is not a three-dimensional object with flat polygon faces and straight edges. It is likely a combination of two-dimensional shapes that have been laid flat.

Explanation:

An example of an object that is not a polyhedron is a sphere. A sphere is a three-dimensional object, but it does not have flat polygon faces and straight edges. Instead, it has a curved surface that does not consist of polygons or flat faces.

To help the learner develop a correct understanding of the concept of polyhedra, you can explain the following properties:

1. A polyhedron is a three-dimensional object.
2. A polyhedron has flat polygon faces.
3. The faces of a polyhedron are connected by straight edges.
4. A polyhedron has sharp corners or vertices where three or more edges meet.

You can also give examples of common polyhedra such as cubes, pyramids, and prisms to reinforce the concept. You can show the learner how to recognize the faces, edges, and vertices of these objects and how they meet at the corners. Additionally, you can demonstrate how to use nets to visualize the three-dimensional object and its faces.

By providing clear explanations and examples, and by using visual aids such as diagrams and nets, you can help the learner develop a correct understanding of the concept of polyhedra and remove any misconceptions or errors they may have.

Answer 2

Answer: To help the learner understand the concept of a polyhedron and correct any misconceptions, I would provide an example of an object that is not a polyhedron. One such object is a cylinder.

A cylinder consists of two circular faces (top and bottom) and one curved rectangular face (the side). Although the cylinder has three faces like the object the learner mentioned, it is not a polyhedron. The key reason for this is that a polyhedron's faces must be polygons—closed shapes with straight sides.

In the case of the cylinder, its curved rectangular face does not meet the requirement of having straight edges. Instead, it has a curved edge connecting the two circular faces. This curved edge makes it impossible to unfold the cylinder into a flat net with straight edges, which is a defining characteristic of polyhedra.

To assist the learner in developing a correct understanding of polyhedra, I would emphasize the following properties:

Faces: A polyhedron must have flat faces that are polygons. These polygons can be triangles, quadrilaterals, pentagons, or any other closed shape made up of straight sides.

Edges: The edges of a polyhedron are straight line segments where the faces meet. These edges should not curve or bend.

Vertices: Polyhedra have sharp corners where the edges meet. These corners are called vertices.

Unfoldability: A polyhedron can be unfolded into a flat net without any overlapping or gaps, while still preserving the shape and size of its faces and edges.

By explaining these properties and using examples like cubes, pyramids, and prisms, I would help the learner differentiate between polyhedra and objects like the cylinder. Additionally, I would encourage the learner to explore various three-dimensional objects and identify their faces, edges, and vertices to reinforce the understanding of polyhedra.

Explanation: